Wilpen Corporation, a price-setting form, manufactures nearly 80% of all tennis balls purchased in the United States. Wilpen estimates the U.S. demand for its tennis balls by using the linear specifications:
Q = a +bp+cm+dpr
Where Q is the number of cans of tennis balls sold quarterly, P is the wholesale price Wilpen charges for a can of tennis balls, M is the consumer's average household income, and Pr is the average price of tennis rackets. The regression results are as follows:
Dependent Variable : Q
R-Square: 0.8435
F- Ratio: 28.75
P-Value on F: 0.001
Observations: 20
Variable Parameter Standard T-Ratio P-Value
Estimate Error
Intercept 425120.0 220300.0 1.93 0.0716
P -37260.6 12587 -22.96 0.0093
M 1.49 0.3651 4.08 0.0009
PR -1456.0 460.75 -3.16 0.0060
a. Discuss the statistical significance of the parameter estimates â, b, c, and d using the p-values. Are the signs of b, c, and d consistent with the theory?
Wipen plans to charge a wholesale price of $1.65 per can. The average price of a tennis racket is $110, and consumers average household income is $24,600.
b. What is the estimated number of cans of tennis balls demanded?
c. At the values of P, M, and Pr given, what are the estimated values of the price (E), income (Em), and cross-price elasticities (Exr) of demand?
d. What will happen, in the percentage of terms, to the number of cans of tennis balls demanded if the price of tennis balls increase 15%?
e. What will happen, in percentage of terms, to the number of cans of tennis balls demanded if the average household income increase 20%?
f. What will happen, in percentage of terms, to the number of cans of tennis balls demanded if the average price of tennis rackets increase by 20 %?